In an overlapping-generations model with non-constant population growth, households own a natural renewable resource and have a family-altruism resource bequest motive. The natural resource can be either extracted and sold to firms, or bequeathed to children to increase their adult disposable income. Numerical applications show how family altruism interplays with population growth to shape the whole economy. The role of altruism in the case of two negative demographic shocks shows that the pressure on the natural resource is not necessarily reduced when population size is lower. Transmission mechanisms between generations and general equilibrium effects can yield unexpected outcomes. In particular, family altruism can lead either to preserve or to waste the resource.